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Computer Science and Information Engineering, World Congress on (2009)
Los Angeles, California USA
Mar. 31, 2009 to Apr. 2, 2009
ISBN: 978-0-7695-3507-4
pp: 335-339
The rough set theory proposed by Pawlak, is a generalization of the classical set theory. Many important algebraic structures are naturally endowed with two binary operations: addition and multiplication, for example, rings, groups and modules. A vector space is an algebraic structure with a binary operation and a multiplication by a scalar. This paper concerned a relationship between rough sets and vector spaces. We considered a vector space as an universal set, and assumed that the knowledge about objects should be restricted by a subspace. First, we discussed relationships between congruences and subspaces of a vector space. Then we defined a pair of rough approximation operators based on a subspace, and obtained some properties of lower (upper) approximation of non-empty subsets of the vector space. Some characterizations of the approximation operators are expressed, and some counter examples are given.

X. Xie, M. Wu and C. Cao, "Rough Subset Based on Congruence in a Vector Space," 2009 WRI World Congress on Computer Science and Information Engineering, CSIE(CSIE), Los Angeles, CA, 2009, pp. 335-339.
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